A142727 For definition see Comments lines.

1, 2, 3, 4, 6, 6, 8, 8, 9, 12, 12, 14, 15, 16, 16, 18, 20, 20, 22, 24, 24, 24, 25, 27, 30, 30, 30, 32, 32, 32, 36, 36, 39, 40, 42, 42, 44, 45, 46, 48, 48, 48, 50, 50, 52, 52, 55, 59, 60, 60, 60, 60, 60, 64, 64, 66, 66, 67, 69, 70, 71, 72, 75, 76, 76, 78, 80, 81, 84

Offset

1,2

Comments

S is a sequence of numbers with repetitions, sorted in nondecreasing order.

Initially a(1) = 1 and S = N = {1,2,3,4,5,6,...}.

For each n >= 2, let p = prime(n), let a(n) = (p-1)st term of S and set S = S union a(n)*N. Repeat.

A sequence arising from one possible attempt to analyze A141586.

Links

David Applegate, Table of n, a(n) for n = 1..1000

David Applegate, Table of n, p(n), a(n), a(n)/n at intervals of 10000 up to 244190000

Formula

A plot of the extended sequence suggests that a(n) ~= c n log(log(n)) + d n for constants c and d. For example, run: $ gnuplot> plot [] [1.27:1.35] a142727.txt using 1:4, 1.12+0.076*log(log(x)).

Example

The first few stages in the calculation are as follows:
S = 1 2 3 4 5 6 7 8 9 10 11 12 13 14 ...
n = 2, p = 3, so a(2) is the 2nd term of S, which is 2.
Now S = 1 2 2 3 4 4 5 6 6 7 8 8 9 10 10 11 12 12 13 14 14 ...
n = 3, p = 5, so a(3) is the 4th term of S, which is 3.
Now S = 1 2 2 3 3 4 4 5 6 6 6 7 8 8 9 9 10 10 11 12 12 12 13 14 14 ...
n = 4, p = 7, so a(4) is the 6th term of S, which is 4.
Now S = 1 2 2 3 3 4 4 4 5 6 6 6 7 8 8 8 9 9 10 10 11 12 12 12 12 13 14 14 ...
n = 5, p = 11, so a(5) is the 10th term of S, which is 6.
And so on.

Crossrefs

Sequence in context: A214965 A350786 A134361 * A347388 A112275 A335876

Adjacent sequences: A142724 A142725 A142726 * A142728 A142729 A142730

Keyword

nonn

Author

David Applegate and N. J. A. Sloane, Oct 03 2008

Status

approved